`P` is a point inside the rectangle ABCD such that `PA=2`, `PB=9`, `PC=10` & `PD= sqrt k` then `"k"` is equal

O is any point inside a rectangle ABCD. Prove that O B^2+O D^2=O A^2+O C^2 .

O is any point inside a rectangle ABCD. Prove that O B^2+O D^2=O A^2+O C^2 .

Let G be the centroid of the DeltaABC , whose sides are of lengths a,b,c. If P be a point in the plane of triangleABC , such that PA=1,PB=3, PC=4 and PG=2 , then the value of a^(2)+b^(2)+c^(2) is

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the question: Let PA=4 , PB=3 cm and CD is diameter of the circle having the length 8 cm. If PC gt PD , then (PC)/(PD) is equal to

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the questions If log_(PA) x=2 , log_(PB)x=3, log_(x) PC=4 , then log_(PD) x is equal to

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the questions If PA=| cos theta + sin theta | and PB=| cos theta - sin theta | , then maximum value of (PC)(PD) , is equal to

Let P be the point inside that Delta ABC. Such that angle APB=angle BPC=angle CPA. Prove that PA+ PB +PC =sqrt((a^(2)+b^(2)+ c^(2))/(2)+ 2sqrt3Delta,)where a,b,c Delta are the sides and the area of Delta ABC.

A point P moves inside a triangle formed by A(0,0),B(1,sqrt(3)),C(2,0) such that min {PA,PB,PC)=1 , then the area bounded by the curve traced by P, is

PA and PB are two tangents drawn from point P to circle of radius 5 . A line is drawn from point P which cuts at C and D such that PC=5 and PD=15 and angleAPB= theta . On the basis of above information answer the questions . Area of DeltaAPB is

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)